A meridional cut of the magnetic field reconstructed from our optimised PFSS model, described in section , is shown for heights below \(2.1R\odot \)  in figure REF  and inside the range of Carrigton longitudes sampled by PSP. State 1, identified as emerging from the vicinity of the main streamer (typically magnetic field line A, in red), presents a denser plasma, embedded in a lower magnetic field than state 2, identified as emerging from an equatorial coronal hole (typically magnetic field line B, in blue on figure REF ). This observation is coherent with past observations of plasma coming from the tip of streamers and pseudo streamers compared with the solar wind emerging from coronal holes [1]}, [2]}, [3]}. If not due to calibration issues, temperature-speed (T-V) relationships revealed that the slope of the T-V relationship is different from state 1 to state 2, and that the speed at which the temperature of protons exceeds the temperature of electrons (which is of 500 km/s at 1 AU [4]}) is faster in the coronal-hole-like plasma (state 2) than in the streamer-like plasma (state 1). From the single fluid simulations, it seems that plasma state 2 (i.e. originating from the coronal hole) is hotter and faster than plasma state 1 at a given altitude above the source surface. As from PSP data, electron temperature is not changing from plasma state 1 to plasma state 2, it can be deduced that the change in temperature observed in the simulations has to be supported by protons in the real solar wind. Thus, the speed at which proton temperature exceeds that of the electrons should be systematically higher in state 2 than in state 1. This suggests that the T-V relation measured in the slow winds bears some dependence on the source region, in addition to the radial evolution already stated by [5]} and revisited through PSP data by [6]}. As explained by [7]}, the T-V relationship in plasma flowing along open magnetic field lines can provide information on the acceleration and heating processes near the Sun, which could suggest that states 1 and 2 are built through different heating processes very low in the solar corona. In the numerical simulations (see profiles on Figure REF ), this difference of temperature is clear above \(2.1R\odot \) . As in red profiles the magnetic field is more intense from the photosphere to \(0.1R\odot \) , and as the expansion factor is higher at almost all altitudes between \(0R\odot \)  and \(1R\odot \) , the heating flux, defined by equation [REF ], remains elevated in red profiles below the altitude of \(1.1R\odot \) . This explains why the temperature is higher along red profiles than along blue profiles below \(1.1R\odot \) . However, above \(2.1R\odot \)  from the center of the Sun, the heating flux drops much faster (i.e. at lower altitude) along red profiles compared to blue profiles. Moreover, the stronger heating at the coronal base has increased the rate of chromospheric evaporation which means that more matter travels along red profiles in the upper corona (as revealed by the density profiles). Beyond the altitude of \(1.1R\odot \) , the heating flux is low due to the high expansion factor which reduces the available energy per particle, resulting in lower temperatures along red profiles than along blue profiles above the Potential Field Source Surface. A quick analysis of the proxy of suprathermal electrons' temperature revealed that state 2 may contain cooler suprathermal electrons than state 1, which would be coherent with the analysis from [8]} conducted on PSP first perihelion, when the spacecraft was briefly connected to an equatorial coronal hole [9]}.
